Algebraic Geometry : An Introduction

Daniel Perrin

ISBN 10: 1848000553 / ISBN 13: 9781848000551

Editore: Springer London, Springer London, 2008

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Druck auf Anfrage Neuware - Printed after ordering - This book is built upon a basic second-year masters course given in 1991- 1992, 1992-1993 and 1993-1994 at the Universit e Paris-Sud (Orsay). The course consisted of about 50 hours of classroom time, of which three-quarters were lectures and one-quarter examples classes. It was aimed at students who had no previous experience with algebraic geometry. Of course, in the time available, it was impossible to cover more than a small part of this eld. I chose to focus on projective algebraic geometry over an algebraically closed base eld, using algebraic methods only. The basic principles of this course were as follows: 1) Start with easily formulated problems with non-trivial solutions (such as B ezout's theorem on intersections of plane curves and the problem of rationalcurves).In1993-1994,thechapteronrationalcurveswasreplaced by the chapter on space curves. 2) Use these problems to introduce the fundamental tools of algebraic ge- etry: dimension, singularities, sheaves, varieties and cohomology. I chose not to explain the scheme-theoretic method other than for nite schemes (which are needed to be able to talk about intersection multiplicities). A short summary is given in an appendix, in which special importance is given to the presence of nilpotent elements. 3) Use as little commutative algebra as possible by quoting without proof (or proving only in special cases) a certain number of theorems whose proof is not necessary in practise. The main theorems used are collected in a summary of results from algebra with references. Some of them are suggested as exercises or problems.

Codice articolo 9781848000551

Dati bibliografici

• Titolo: Algebraic Geometry : An Introduction
• Editore: Springer London, Springer London
• Data di pubblicazione: 2008
• Lingua: Inglese
• ISBN 10: 1848000553
• ISBN 13: 9781848000551
• Rilegatura: Taschenbuch
• Condizione: Neu

Descrizione articolo

Riassunto

Aimed primarily at graduate students and beginning researchers, this book provides an introduction to algebraic geometry that is particularly suitable for those with no previous contact with the subject; it assumes only the standard background of undergraduate algebra. The book starts with easily-formulated problems with non-trivial solutions and uses these problems to introduce the fundamental tools of modern algebraic geometry: dimension; singularities; sheaves; varieties; and cohomology. A range of exercises is provided for each topic discussed, and a selection of problems and exam papers are collected in an appendix to provide material for further study.

Dalla quarta di copertina

Aimed primarily at graduate students and beginning researchers, this book provides an introduction to algebraic geometry that is particularly suitable for those with no previous contact with the subject and assumes only the standard background of undergraduate algebra. It is developed from a masters course given at the Université Paris-Sud, Orsay, and focusses on projective algebraic geometry over an algebraically closed base field.

The book starts with easily-formulated problems with non-trivial solutions – for example, Bézout’s theorem and the problem of rational curves – and uses these problems to introduce the fundamental tools of modern algebraic geometry: dimension; singularities; sheaves; varieties; and cohomology. The treatment uses as little commutative algebra as possible by quoting without proof (or proving only in special cases) theorems whose proof is not necessary in practice, the priority being to develop an understanding of the phenomena rather than a mastery of the technique. A range of exercises is provided for each topic discussed, and a selection of problems and exam papers are collected in an appendix to provide material for further study.